I may have fixed it. I was reading about oven issues and a common theme was the pilot/thermocouple interface was not set correctly. So I looked at mine and the pilot flame and thermocouple were about one half inch apart. With that distance, I had to hold down the pilot button too long in order for the pilot to stay lit so I bent the two till they were about one quarter inch apart.
After that, I only had to hold down the pilot button for about 10 seconds for the pilot to stay lit. As it stands, the thermocouple is directly in the flame (not at the tip of the flame) and the flame flows around both sides of the thermocouple.
So then I tested the oven by setting it at 300 and waiting the requisite 10 minutes. Boom, it was at 300. I then set the oven at 350 and decided I would let it cycle on and off for a bit so I came back in 15 minutes. Low and behold, it was at 350.
Of course, this is only one sample but I like the trend. I'll keep my fingers crossed.